Question: Assume that y = sin -1 x is a differentiable function of x. By differentiating the equation x = sin y implicitly, show that dy/dx

Assume that y = sin-1 x is a differentiable function of x. By differentiating the equation x = sin y implicitly, show that dy/dx = 1/√1 - x2.

Step by Step Solution

★★★★★

3.49 Rating (152 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

ANSWER We start by differentiating the equation x sin y implicitly with respect to x Using the cha... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Precalculus Questions!

Q:

Use the formula in Exercise 55 to find dy/dx if a. y = (sin -1 x) 2 b. Exercise 55 Assume that y = sin -1 x is a differentiable function of x. By differentiating the equation x = sin y implicitly,...

Q:

Alejandro Puron recently encountered a dilemma in working with his quality circle (QC) team. One of the team members claims that the QC must always be unanimous in its recommendations....

Q:

A)Begin by differentiation each side of the equation x=siny. Findd/dxB) Find d/dx sinyC) Find dy/dx Assume that \( y=\sin ^{-1} x \) is a differentiable function of \( x \). By differentiating the...

Q:

Find dy / dx in terms of x and y if cos 2 (2 y )+sin 2 (2 y )= y +9 . (1 point) Find dy/dx in terms of x and y if cos? (2y) + sin (2y) = y + 9. dy dx(1 point) Find the slope of the tangent line to...

Q:

40. Find dy in terms of x and y for the function x + y = 6. dx y a. . X b. 6 dy 2 X N - + y c . a dy y dy 2 12 d. dry dx 2 d'y y e. dx 2 41. The function f(x) = x has two tangents drawn to it at the...

Q:

4. Which of the following statements is correct? a. The derivative of a product is the product of the derivatives. b. The derivative of a quotient is the quotient of the derivatives. c. The...

Q:

\f6) Suppose f (x) is a differentiable function such that f (1) = 7 and f'(1) = 2. Use a tangent line approximation to estimate f (0.8).\fQ) The table below gives specific values for a differentiable...

Q:

ULUS WRITTEN WORK #3 NAME SECOND GRADING, 1" SEMESTER GRADE & SECTION: DATE: General Instructions: This is a Quiz worth 30 points from module 6, Detach the 2 pages and staple them together. pages....

Q:

# 7 (chapter 5)(40 points, Due on Friday November 11) Question 1. [3 points each] Use the definition of Limit of functions to prove that x2 2 . 5 5 2 lim x 3 x 1 1 (B) x 1 (A) lim x 0 if x 2 2x (C)...

Q:

MATH 140 EXAM 1 Oct-Dec 2016 NAME Professor:B. Stec INSTRUCTIONS The exam is worth 100 points. There are 10 problems and one extra credit worth 5pts. This exam is open book and open notes with...

Q:

To solve the equation -4(x+y)=12x-16y for x, fill in the expressions that correctly complete the steps of the solution.

Q:

At the room temperature (25 C), ethene can be hydrogenated (add one mole of H to the double bond) to give ethane in the presence of a catalyst, as shown below: H H C=C H ethene + H catalyst 25 C HH...

Q:

The type of statement that returns a value from a function is the a . break statement b . if - else statement c . while statement d . return statement

Q:

EXERCISE 12.1. Consider the autocatalytic nonlinear chemical reaction The affinity can be written A = RT In(kc/k2CBCx), where CB (cx) is the molar density of chemical B(X). (a) When the molar...

Q:

Sketch the graph of a function f where the domain is (-2, 2), f is continuous at all numbers in its domain except 1, and f is odd. F'(0) = -2, lim,-2-f(x) = , f

Q:

Evaluate the limit, if it exists. 4 - Vx lim x16 16x x?

Q:

Explain, using Theorems 4, 5, 7, and 9, why the function is continuous at every number in its domain. State the domain. x? + 1 G(x) 2x2 1

Q:

Durango Mountain Bike Tours' ending cash balance as of December 31, 2020 was $10,000. Its expected cash collections and payments for the next six months are given in the following table. a. Calculate...

Q:

On January 1, 2015, Ackerman sold equipment to Brannigan (a wholly owned subsidiary) for $350,000 in cash. The equipment had originally cost $330,000 but had a book value of only $255,000 when...

Q:

XYZ company has two product lines, wholesale and retail. The retail product line appears to be losing money, and is being considered for elimination. If the retail line is dropped, its salaries and...